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Question

The number of words, that can be formed by using all letters of the word DAUGHTER, if relative order of vowels and consonants remains same, are


A
2880
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B
6720
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C
720
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D
3600
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Solution

The correct option is C $$720$$
The given word consist of 8 different letters in which $$3$$ are vowels and $$5 $$ are consonants.
The relative position of vowel and consonants remain same means that vowel can take place of vowel and consonants to take place of consonants.
Now the $$3$$ vowels can be arranged among themselves in $$3!=3!2!1!=6$$ ways
The $$5$$ consonants can be arranged among themselves in $$5!=5!4!3!2!1!=120 $$ways
$$\therefore $$The total numbers of words that  can be formed$$=120\times 6=720$$ 

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